Convert the following measurements from scientific notation to standard notation.(a) 3.221 * 10-3 mm (b) 8.940 * 105 m (c) 1.350 82 * 10-12 m3 (d) 6.4100 * 102 km

Verified step by step guidance

1. Identify the exponent in the scientific notation for each measurement.
2. For each measurement, determine if the exponent is positive or negative.
3. If the exponent is positive, move the decimal point to the right by the number of places equal to the exponent.
4. If the exponent is negative, move the decimal point to the left by the number of places equal to the absolute value of the exponent.
5. Write down the resulting number in standard notation for each measurement.

Key Concepts

Scientific Notation

Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form. It is represented as a product of a number (between 1 and 10) and a power of ten. For example, 3.221 × 10^-3 means 3.221 divided by 1000, which simplifies calculations and comparisons of very large or small values.

Standard Notation

Standard notation is the conventional way of writing numbers using digits without exponents. It represents the actual value of a number in a straightforward manner. Converting from scientific notation to standard notation involves calculating the power of ten and adjusting the decimal point accordingly, making the number easier to read and interpret.

Exponent Rules

Exponent rules are mathematical guidelines that dictate how to handle powers of ten during calculations. For instance, when multiplying or dividing numbers in scientific notation, you add or subtract the exponents, respectively. Understanding these rules is crucial for accurately converting between scientific and standard notation, especially when dealing with positive and negative exponents.